A Boolean lattice has a number of rather nice properties which give it a central role in many parts of combinatorics. For instance, it's a lattice, it can be augmented with a ring structure, it can ...
Because I have heard the phrase "totally ordered abelian group", I imagine there should be non-abelian ones. By this I mean a group with a total ordering (not to be confused with a well-ordering) ...
It is easy to see that the totally ordered group Z (the integers) with the natural order has no non-trivial automorphisms. Is this also true for Z^n with the lexicographical order?
I feel a little embarrassed to be asking this question here, since I think it should be much easier than I'm making it, but here goes: Given a finite poset P, does there necessarily exist some chain ...
This question is based on a blog post of Qiaochu Yuan. Let P be a locally finite* graded poset with a minimal element, and w be a weight function on the elements of P. Suppose that the total weight ...
Three problems from G.Rosenstein "Linear orderings" (from the end of Chapter 2 and beginning of Chapter 4): 1) Is there a nondecreasing function from irrationals onto reals? 2) Is there a ...